# Credit Card Fraud Detection and Concept-Drift Adaptation with Delayed Supervised Information

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1 Credit Card Fraud Detection and Concept-Drift Adaptation with Delayed Supervised Information Andrea Dal Pozzolo, Giacomo Boracchi, Olivier Caelen, Cesare Alippi, and Gianluca Bontempi 15/07/2015 IEEE IJCNN 2015, Killarney, Ireland 1/ 22

2 INTRODUCTION Fraud Detection is notably a challenging problem because of concept drift (i.e. customers habits evolve) class unbalance (i.e. genuine transactions far outnumber frauds) uncertain class labels (i.e. some frauds are not reported or reported with large delay and few transactions can be timely investigated) 2/ 22

3 INTRODUCTION II Fraud-detection systems (FDSs) differ from a classification tasks: only a small set of supervised samples is provided by human investigators (they check few alerts). the labels of the majority of transactions are available only several days later (after customers have report unauthorized transactions). 3/ 22

4 PROBLEM FORMULATION We formalise FD as a classification problem: At day t, classifier K t 1 (trained on t 1) associates to each feature vector x R n, a score P Kt 1 (+ x). The k transactions with largest P Kt 1 (+ x) define the alerts A t reported to the investigators. Investigators provide feedbacks F t about the alerts in A t, defining a set of k supervised couples (x, y) F t = {(x, y), x A t }, (1) F t are the only immediate supervised samples. 4/ 22

5 PROBLEM FORMULATION II At day t, delayed supervised couples D t δ are transactions that have not been checked by investigators, but their label is assumed to be correct after that δ days have elapsed. Supervised%samples% t δ Time% t 1 t D t δ F t Delayed%samples% Feedbacks% All%fraudulent%transac9ons%of%a%day% All%genuine%transac9ons%of%a%day% Fraudulent%transac9ons%in%the%feedback% Genuine%transac9ons%in%the%feedback% Figure : The supervised samples available at day t include: i) feedbacks of the first δ days and ii) delayed couples occurred before the δ th day. 5/ 22

6 F t are a small set of risky transactions according the FDS. Fraudulent%transac9ons%in% S D t δ contains all the occurred t Genuine%transac9ons%in% S t transactions in a day ( 99% genuine transactions). Fraudulent%feedback%in%% F t Genuine%feedback%in%% F t Time% F t 1 D t 7 F t 6 F t 5 F t 4 F t 3 F t 2 F t Day'1' D t 8 F t 1 D t 7 F t 6 F t 5 F t 4 F t 3 F t 2 F t Day'2' D t 9 D t 8 F t 1 D t 7 F t 6 F t 5 F t 4 F t 3 F t 2 F t Day'3' Figure : Everyday we have a new set of feedbacks (F t, F t 1,..., F t (δ 1) ) from the first δ days and a new set of delayed transactions occurred on the δ th day (D t δ ). In this Figure we assume δ = 7. 6/ 22

7 ACCURACY MEASURE FOR A FDS The goal of a FDS is to return accurate alerts, thus the highest precision in A t. This precision can be measured by the quantity p k (t) = #{(x, y) F t s.t. y = +} k (2) where p k (t) is the proportion of frauds in the top k transactions with the highest likelihood of frauds ([1]). 7/ 22

8 LEARNING STRATEGY Learning from feedbacks F t is a different problem than learning from delayed samples in D t δ : F t provides recent, up-to-date, information while D t δ might be already obsolete once it comes. Percentage of frauds in F t and D t δ is different. Supervised couples in F t are not independently drawn, but are instead selected by K t 1. A classifier trained on F t learns how to label transactions that are most likely to be fraudulent. Feedbacks and delayed transactions have to be treated separately. 8/ 22

9 CONCEPT DRIFT ADAPTATION Two conventional solutions for CD adaptation are W t and All%fraudulent%transac9ons%of%a%day% E t [6, 5]. To learn All%genuine%transac9ons%of%a%day% separately from feedbacks and delayed transactions Fraudulent%transac9ons%in%the%feedback% we propose F t, Wt D and Et D. Genuine%transac9ons%in%the%feedback% Time% D t 8 F t 1 D t 7 F t 6 F t 5 F t 4 F t 3 F t 2 F t Sliding' window' W D t F t W t D t 8 F t 1 D t 7 F t 6 F t 5 F t 4 F t 3 F t 2 F t Ensemble' M 2 M 1 F t E D t E t 9/ 22 Figure : Supervised information used by different classifiers in the ensemble and sliding window approach.

10 CLASSIFIER AGGREGATIONS W D t and E D t have to be aggregated with F t to exploit information provided by feedbacks. We combine these classifiers by averaging the posterior probabilities. Sliding window: P A W t (+ x) = P F t (+ x) + P W D t (+ x) 2 Ensemble: P A E t (+ x) = P F t (+ x) + P E D t (+ x) 2 A E t and A W t give larger influence to feedbacks on the probability estimates w.r.t E t and W t. 10/ 22

11 TWO RANDOM FOREST We used two different Random Forests (RF) classifiers depending on the fraud prevalence in the training set. for classifiers on delayed samples we used a Balanced RF [3] (undersampling before training each tree). for F t we adopted a standard RF [2] (no undersampling). 11/ 22

12 DATASETS We considered two datasets of credit card transactions: Table : Datasets Id Start day End day # Days # Instances # Features % Fraud ,830, % ,619, % In the 2013 dataset there is an average of 160k transaction per day and about 304 frauds per day, while in the 2014 dataset there is a daily average of 173k transactions and 380 frauds. 12/ 22

13 EXPERIMENTS Settings: We assume that after δ = 7 days all the transactions labels are provided (delayed supervised information) A budget of k = 100 alerts that can be checked by the investigators (F t is trained on a window of 700 feedbacks). A window of α = 16 days is used to train Wt D in Et D) (16 models Each experiments is repeated 10 times and the performance is assessed using p k. 13/ 22

14 In both 2013 and 2014 datasets, aggregations A W t outperforms the other FDSs in terms of p k. and A E t Table : Average p k in all the batches for the sliding window Dataset 2013 Dataset 2014 classifier mean sd mean sd F W D W A W Table : Average p k in all the batches for the ensemble Dataset 2013 Dataset 2014 classifier mean sd mean sd F E D E A E / 22

15 A W F W W D (a) Sliding window 2013 A W F W W D (b) Sliding window 2014 Sum of ranks from the Friedman test [4], classifiers having the same letter are not significantly different (paired t-test based upon on the ranks). A E F E E D A E F E E D (c) Ensemble 2013 (d) Ensemble / 22

16 EXPERIMENTS ON ARTIFICIAL DATASET WITH CD In the second part we artificially introduce CD in specific days by juxtaposing transactions acquired in different times of the year. Table : Datasets with Artificially Introduced CD Id Start 2013 End 2013 Start 2014 End 2014 CD CD CD / 22

17 Table : Average p k in the month before and after CD for the sliding window approach (a) Before CD CD1 CD2 CD3 classifier mean sd mean sd mean sd F W D W A W (b) After CD CD1 CD2 CD3 classifier mean sd mean sd mean sd F W D W A W / 22

18 A W W A W W (e) Sliding window strategies on dataset CD1 (f) Sliding window strategies on dataset CD2 W AW A E E (g) Sliding window strategies on dataset CD3 (h) Ensemble strategies on dataset CD3 Figure : Average p k per day (the higher the better) for classifiers on datasets with artificial concept drift smoothed using moving average of 15 days. The vertical bar denotes the date of the concept drift. 18/ 22

19 CONCLUDING REMARKS We notice that: F t outperforms classifiers on delayed samples (trained on obsolete couples). F t outperforms classifiers trained on the entire supervised dataset (dominated by delayed samples). Aggregation gives larger influence to feedbacks. 19/ 22

20 CONCLUSION We formalise a real-world FDS framework that meets realistic working conditions. In a real-world scenario, there is a strong alert-feedback interaction that has to be explicitly considered Feedbacks and delayed samples should be separately handled when training a FDS Aggregating two distinct classifiers is an effective strategy and that it enables a prompter adaptation in concept drifting environments 20/ 22

21 FUTURE WORK Future work will focus on: Adaptive aggregation of F t and the classifier trained on delayed samples. Study the sample selection bias in F t introduced by alert-feedback interaction. 21/ 22

22 BIBLIOGRAPHY [1] S. Bhattacharyya, S. Jha, K. Tharakunnel, and J. C. Westland. Data mining for credit card fraud: A comparative study. Decision Support Systems, 50(3): , [2] L. Breiman. Random forests. Machine learning, 45(1):5 32, [3] C. Chen, A. Liaw, and L. Breiman. Using random forest to learn imbalanced data. University of California, Berkeley, [4] M. Friedman. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association, 32(200): , [5] J. Gao, B. Ding, W. Fan, J. Han, and P. S. Yu. Classifying data streams with skewed class distributions and concept drifts. Internet Computing, 12(6):37 49, [6] D. K. Tasoulis, N. M. Adams, and D. J. Hand. Unsupervised clustering in streaming data. In ICDM Workshops, pages , / 22

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